A method and a device for reducing speckle formation on a projection display when working with a coherent light source. In this context, the light coming from the light source, before the projection, may strike an electrically controllable optical element having a spatially inhomogeneous refractive index, passing through the same, the refractive index being varied over time within the projection period. This may lead to an averaging out of the speckle pattern on the projection screen. For purposes of illumination, a multimode light source may be used, and/or the light coming from the light source is separated into a plurality of spatial modes, thereby reinforcing the effect. As an optical element, one may employ a liquid crystal element composed of at least two liquid crystal layers, to which a spatially dependent voltage is applied to generate a spatially dependent refractive index. Its birefringence may be compensated by orientating the layers to one another in appropriate fashion.